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In situ testing of barrette foundations for a high retaining wall in Molasse rock

Article  in  Géotechnique · February 2018

DOI: 10.1680/jgeot.17.p.144

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In situ testing of barrette foundations for a high retaining wallin molasse rock

C. RABAIOTTI� and C. MALECKI†

Barrettes are common foundations for high-rise buildings, especially because of their high bearingcapacity, for vertical as well as for lateral loads. In this paper, it is shown how these were adopted andtested for anchoring a 27 m high retaining wall in rock on a slope located in the centre of Zurich. Themonolithic 10� 1� 25 m deep barrettes, excavated and built in layered rock (Upper FreshwaterMolasse), are also intended to stabilise the slope. The main contribution to their bearing capacity isgiven by the contact strength between the reinforced concrete and the rock. Two full-scale pull-out tests,instrumented by distributed fibre-optical measurements, are carried out to investigate the contactstrength between rock and reinforced concrete. The results show that dilatancy at the contact caused bythe irregular excavated surface has a strong influence on the bearing capacity. Additionally, thedistributed fibre-optic instrumentation allowed progressive crack propagation of the reinforced concretein the barrettes to be detected during the test. Inverse analysis of the rock and concrete tensile propertiesare obtained within a finite-element calculation, which takes into account the non-linear properties ofthe reinforced concrete and the rock.

KEYWORDS: bearing capacity; design; diaphragm & in situ walls; excavation; finite-element modelling;full-scale tests

INTRODUCTIONETH Zurich (Swiss Federal Institute for Technology) isbuilding a new research centre for medical technologyresearch and application. The building is located on a slopein the Zurichberg central city quarter (Fig. 1(a)). Thebuildings that were previously located on the site have beendemolished. The new building now under construction isdeeper, and on the north-east side it will have six storeysbelow ground level. As the structure is built on a slope, onlytwo storeys will be below the surface on the south-west side.The architectural design of the main building is limited by

three main considerations. The construction site is located ina very prominent place surrounded by villas. The require-ments of the neighbourhood and the law did not allow thebuilding to be high enough to satisfy all the needs of the newlaboratory and research building. The solution is to builddeep into the ground, causing a one-sided deep cut in theslope. Additionally, the building owner wanted to avoid asolution with permanent anchors for reasons of maintenanceand neighbourhood requirements. The anchors installed toretain the pile wall during excavation should be onlytemporary. The third important characteristic is the archi-tecture and the requirement that the main building shouldhave a light, flexible construction, allowing more space forteaching rooms and laboratories to be obtained. Therefore,it was important not to conduct any forces exerted by theslope through the walls of the structure, so it was necessary todesign an independent retaining structure that was separatefrom the building. These three requirements together ledto a unique slope stabilisation construction consisting of a

retaining wall founded on barrette elements. In order toverify the bearing capacity of the foundation, two small-scalepull-out tests of test barrettes (TBs) were conducted. Theresults of these tests are extensively discussed in this paper.

GEOLOGYThe slope-stabilising wall is built into the Zurichberg hill

(Fig. 1(a)). The slope has an inclination between 23° and 28°towards the south-west. The geological cross-section is shownin Fig. 1(b). The soil consists of an approximately 13 m thickmoraine layer (USCS: SC-SM, GM), which accumulatedthrough the movement of the ancient Linth glacier (lateralmoraine). The upper part of the moraine is slightly less dense,owing to weathering processes. Large boulders can occasion-ally be found inside the soil silty-sand matrix.The soil is underlain by the rock of the Upper Freshwater

Molasse (moderately weak to moderately strong rock(Eurocode 7 (CEN, 2004)) in which excavation can becarried out by ripping), which consists of layers of sandstone(percentage by mass 43%, RQD 85–100%), siltstone (per-centage by mass: 47%, RQD 85–100%) and marl includingfine coal layers (percentage by mass: 10%, RQD 25–60%).The top layers of the rock present vertical joint disconti-nuities which are moderately to highly weathered.Joints occur mainly in sandstone and siltstone layers; marl

shows almost no jointing.In the coal layers, small snail shells can also be found.

The rock is layered in a more or less horizontal direction witha very slight dip. The marl layers represent a potential riskfor slope stability, and their slippage needs to be preventedduring excavation by suitable design of the retainingstructure. This issue is addressed by the wall design describedin the paper. A cross-section of the rock layers at the bottomof the pit (excavation trench of TBs) and pictures from a rockcore drilling are presented in Figs 1(c) and 1(d). Boreholesinstrumented with vibrating wire piezometers showed thatgroundwater is not present in the slope. However, water fromprecipitation can potentially infiltrate into the rock fissures,

� University of Applied Sciences Rapperswil, Rapperswil,Switzerland (Orcid:0000-0002-9618-7273).† Basler & Hofmann AG, Esslingen, Switzerland.

Manuscript received 31 May 2017; revised manuscript accepted10 January 2018.Discussion on this paper is welcomed by the editor.

Rabaiotti, C. & Malecki, C. Géotechnique [https://doi.org/10.1680/jgeot.17.P.144]

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and flow can take place over the impermeable rock surface.A drainage layer will therefore be installed on the temporaryretaining pile wall in order to prevent development ofpore-water pressure behind the permanent retainingstructure.

The parameters for soil and rockobtained by extensive soilinvestigation (GLM Report, 2013) are shown in Table 1. Noangle of dilatancy has been considered for the soil and therock for the foundation design (conservative assumption).

RETAINING WALL CONCEPTThe permanent earth-retaining structure consists of a

reinforced concrete wall (Figs 2(a) and 2(b)). The task ofslope stabilisation is taken over by buttresses founded on

barrettes. Reinforced concrete arches transmit the earth loadsto the buttress like a multiple arch dam. The cavities betweenthe arches and the rear side of the wall, directly supportingthe earth, are adopted as vertical ventilation channels, whichbring clean air into the building. In order to link thefoundation to the wall, six pre-stressed cables are positionedinside the barrette piles. The cables are then conductedthrough the buttresses up to the top of the wall (Figs 2(a)and 2(b)). During construction of the wall, the cables arestep-wise tensioned and the force in the anchors progressivelyremoved.The design of the steel cage was rather complex and is not

described in this paper. The steel cages (25� 10� 1 m,weight = 550 kN; see also Figs 3(a) and 3(b)) were built inone piece on site as monoliths on a steel table, which was later

NETH mainbuilding

Project area andcross-section

Loose moraine

Dense moraine

Silt and sandstone

Weathered rock

Marl (sliding layer)

* = Metres above sea level

Old building

Excavation

462·73* 9 m

17 ÷

19

m

Siltstone

Marl

Sandstone

Coal layer (core cross-section)

Marl layer

(a) (b)

(c)(d)

Fig. 1. (a) Project location; (b) geological section of the excavation; (c) rock layers from trench excavation; (d) rock core (marl) and cross-sectionof coal layer.

Table 1. Geotechnical parameters

Loosemoraine

Densemoraine

Sandstone, moderatelyweathered

Sandstone, highlyweathered

Siltstone Marl Upper FreshwaterMolasse

γ: kN/m3 20 21 25 24·5 25 24 25ϕ′: degrees 32 36 38 34 32 22 28v 0·3 0·3 0·3 0·3 0·3 0·3 0·3c′: kN/m2 0 0 100 15 50 10 30qu: MN/m2 — — 40 15 25 10 35Epl: MN/m2 25 50 2700 2300 1400 460 2500Eur: MN/m2 80 170 — — — — —

The cohesion values for the rock are given for the direction orthogonal to the layers. The contribution of dilatancy was not considered.

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lifted to put them in the upright position. A separate cranetransported the cage to the excavated trench.The design developed for the retaining wall was driven by

the concept of clamping the foundation in the rock, whilepreventing the slippage of the rock layers. To prevent slippageand carry the enormous forces from the slope weight,a foundation structure with a large moment of inertia wasrealised. Fourteen very large barrette foundations werearranged as single elements, with their longest plan dimen-sion parallel to each other at intervals of 7·15 m. Thebarrettes were placed with the direction of their largesthorizontal inertia moment parallel to the slope (see alsoFig. 2(b)). Inside each steel cage, six pre-stressed steel cablesare positioned (see Fig. 3(b)). The pre-stressed cables havetwo main tasks: (a) reducing the wall bending and defor-mation (including concrete creep); (b) ensuring high enoughtensile strength of the barrettes.The geotechnical design was carried out using the

finite-element (FE) code Plaxis (Plaxis3D, 2015). Theresults were validated against simple mechanical models,which resemble the bearing behaviour of standard retainingstructures, such as a cantilever or heavy retaining wall(Figs 4(a) and 4(c)).The FE analysis of the wall and the results are not

described in this paper. Instead, the next section illustratesthe efforts made to validate the results from the numericalcalculation. The results of these analyses showed the needfor in situ testing to assess the bearing capacity of thefoundation.

RETAINING WALL DESIGNThe FE analysis revealed that the behaviour of the

foundation resembles that of a cantilever beam, where thesilt and sandstone layers of the rock react like semi-rigidspring supports (Fig. 4(a)). As intended, the barrettes preventslippage of the layers and induce in each of them an actionand reaction clamping normal force. As a groundwater table

is not present and a drainage system will be installed, nowater pressure was considered in the design calculations.The results from the FE analysis also showed that the shear

contact forces between the sides of the barrettes and the rockare essential for ensuring the wall’s stability and producingthe clamping normal forces. A simple model was thereforedeveloped in order to quantify the shear contact forcesnecessary to stabilise the wall. In the model, a ‘brake’ discidealises the barrettes (Fig. 4(b)). This method allows a verysimple determination of the friction necessary to counter-balance the overturning moment due to weight of the slope.From the idealised model, it was concluded that, if the

barrettes and the rock between them do not slip relative toeach other (like a brake disc), the wall behaves like a heavyretaining wall (Fig. 4(c)). From the polygon of forces(equilibrium of the action and reaction forces), all the forcecomponents acting on the wall can be easily determined. Theminimum contact shear strength for equilibrium (withoutsafety factors) between the wall and the rock was quantifiedas 160 kN/m2. For design, a minimum contact shear strengthof 360 kN/m2 was required. The factors of safety wereadopted from the Swiss standard SN SIA 267 (SIA, 2013a).

REVIEWOF RESISTANCE OF SHAFTS IN ROCKThe bearing capacity of shafts in rock has been extensively

studied in the past. In the literature, several approaches forpredicting shaft resistance of piles can be found. Well-knownmethods are based on empirical approaches in which theshaft resistance is generally described by empirical functionsrelated to the uniaxial compressive strength of the material(Pells et al., 1980; Horvath et al., 1983; Rowe & Armitage,1984; Reese & O’Neill, 1988; Kulhawy & Phoon, 1993).These approaches have also been modified with coefficientsfor taking into account socket roughness factors (Seidel &Collingwood, 2001). A different approach was followed bySerrano & Olalla (2004, 2006), who developed and validateda prediction method based on the Hoek and Brown failure

25 m

10 m

10 m

17·5 m

A A

4·5 m

Prestressing cables

Piles

3 m

Temporaryanchors

2·35 mA

A1·0 m

7·15 m

Piles

Temporaryanchors

Prestressing cables

Ventilation channels

Barrette

(a)

(b)

Fig. 2. (a) Vertical cross-section and (b) horizontal cross-section of the retaining wall

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 3

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criterion. More rigorous methods based on elastic andelastoplastic solutions were proposed by Rowe & Armitage(1986), Carter & Kulhawy (1988) and Kulhawy & Carter(1992).

The analytical approach followed in this paper is the onedescribed by Kulhawy & Carter (1992). They developed amethod based on an elastoplastic solution, which takesinto account the effects of cohesion, friction and dilatancyfor the bearing capacity of shafts socketed into rock. Thepredictions resemble quite well the foundation bearingbehaviour observed in this study, although, in the presentcase, a more complex interaction between the rock and thestructure was observed, because of the non-linear behaviourof the reinforced concrete. Exhaustive interpretation of thetest results was therefore carried out with non-linear FEanalysis, which takes into account the observed non-linear

behaviour of rock and reinforced concrete. Additionally, thetraditional approach described by Fleming (1992) based onChin hyperbolic functions was adopted to extrapolate thefailure load from experimental results.Generally, bearing capacity tests of barrettes are less

common than pile testing, and not many examples can befound in the literature. A good example of a conventionalhead-down static load test on a barrette foundation can befound in Musarra & Massad (2015). For very high loads,static load tests are nowadays often carried out with O-cells(Osterberg, 1998; Fellenius & Ann, 2010). In the presentstudy, the results and the interpretation of a conventionalhead-down pull-out test are presented.

IN SITU BEARING CAPACITY TESTSAs explained in the previous sections, the verification of

admissible contact forces between the barrette and the rock iscrucial to determine the safety of the retaining wall. Two insitu pull-out tests were therefore designed and built with theaim of determining the contact strength between the rockand the barrette. The two tests were carried out on oppositesides of the excavations (Fig. 5(a)). This allowed two differentextremes of the geology to be studied and, thanks to therepetition of the test, allowed reliable results to be obtained.The TBs were built inside an excavated trench at a depth ofbetween 9 and 12·5 m (Fig. 5(b)). The excavation for buildingthe TB took place from the level corresponding to the head ofthe wall barrette foundation. Therefore, the vertical positioncorresponds to the location at which the highest shear forcedue to the rotation of the foundation is expected.The trench was excavatedwith a Bauer trench cutter BC-40

and bentonite mud conveyor. The bentonite had a density of1·05 kN/m3 and Marsh funnel time equal to 32 s. Twooverlapping trenches of 2·8 m were excavated in order toobtain the desired size of 4·7 m (longest dimension). Thesame device and techniques were adopted for excavating thebarrettes for the foundation of the retaining wall. The TBswere cast on 9 (TB2) and 10 October 2016 (TB1), and thetests took place on 21 and 23 November 2016, respectively.The trenches were wider at the top, down to a depth of 9 m

(4·7 m long and 1·2 m wide), whereas the trench where theTBs were cast had a length of 3·7 m and a width of 1 m(Fig. 6(a)). The TBs had a depth of 3·5 m, a length of 3 mand a width of 1 m. A 35 cm wide separation was realisedbetween the shortest side of the TBs and the rock by adoptingsheet piling steel profiles during casting. These were removedafter the concrete had cured. Therefore, the TB was only incontact with the rock on the longer side of its horizontalcross-section. This particular geometry of the excavationtrench was realised in order to prevent wedging of the wallduring the pull-out.The TBs were pulled out through eight GEWI bars (dia.

63·5 mm), which were anchored at the bottom of the steelcages with steel plates. The barrettes were additionallyreinforced with horizontal and vertical steel rebars with adiameter of 20 mm at 25 cm spacing. Each GEWI steel barwas connected on the top to a hydraulic press (eight presses intotal) which was able to apply a maximum theoretical load of2 MN (total maximum load 16 MN) (Fig. 6(b)). Themaximum applicable load was limited to 12 MN becauseof the steel frame adopted.Most of the bentonite mud had been removed before the

test was carried out, in order to observe the roughness of theexcavated surface and the quality of the rock, leaving onlyapproximately 2·5 m of the bentonite suspension above theupper side of the barrette. The reason for not removing allthe bentonite was that rock blocks and debris were fallinginto the excavation, and there was concern about damaging

(a)

(b)

Fig. 3. (a) Monolithic 10× 25 m steel cage and (b) close view of thepre-stressed cable during installation (author: Niklas Haag,Bauer AG)

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the instrumentation, in particular the fibre-optic cables.Additionally, fissure water stored in the rock was refillingthe excavation and causing lateral surface instabilities. Thissmall source of water was occasionally observed in rockfissures and was probably caused by precipitation (GLMReport, 2013).Figures 7(a)–7(e) show the steel cages of the TBs, the

excavated trench, the casting of the TBs and the steel frameadopted for the loading. Fig. 7(b) shows in particular that thesurface of the excavated rock had quite a high roughness,especially due to the loosening of the marl layers duringexcavation.

InstrumentationThe installed instrumentation is listed below.

(a) Eight load cells placed on the GEWI steel profiles(precision 1 kN) for measuring the total load.

(b) One linear variable differential transformer (LVDT) ona GEWI profile for measuring the strains in the steel.

(c) Eight LVDTs for measuring the horizontaldeformation of the guide walls.

(d ) Two LVDTs on two Tremie pipes, fixed on thereference beam, for measuring the uplift of the TB(see also Fig. 7(e)).

(e) Two surveyor’s levels (one of them fully automatic),precision 1/100 mm. These devices allowedmeasurements of the movements of the steel frame,the concrete basements and the reference beamdisplacement.

( f ) Two fibre-optic cable loops inside the TB (BRUsensBSST-V9: armoured fibre-optic strain sensing cableswith central metal tube protecting one tight-bufferedoptical fibre, structured polyamide outer sheath,allowing a typical measurement strain range up to 1%).

(g) Oil pressure sensor inside each hydraulic press.

A closer look at a part of the LVDTs adopted for measuringthe uplift is given in Fig. 7(e). The most difficult challenge

E0E0 EA1

EA1 EA2,HG1

G2

EA2,V

EA2,V

EA2,H EP2,H

EP2,V

R2

EP2,V

EP2,H

R1G1

G2

R1

8·7 m

13·8 m

R eq.

T

T

Main buildingraft foundation

Potential slidinglayers (marl)

(a)

(b)

(c)

Fig. 4. Simple mechanical model for validating the FE calculation: (a) cantilever beam model; (b) mechanical model for obtaining requirednecessary rock–concrete contact strength for the stability; (c) heavy wall model and equilibrium of the external forces

Barrette foundation

TB 1 TB 2

Level of the excavation for TBs

9·0 m

1·0 m

1·0 m

Final level of theexcavation

TB

Barrette foundation

(a)

(b)

Fig. 5. (a) Positions of the two tests in the excavation pit and(b) vertical cross-section of the TB

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 5

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for the instrumentation was to measure the vertical move-ment of the TB. Since the expected displacements were verylow, the precision of the measurement had to be on the orderof 1/100 mm. On top, the uplift had to be measured at 9 mdepth directly on the surface of the TB. Therefore, it wasdecided to put two heavy and rigid tremie pipes on top of theTBs and to measure their vertical movement during the test.This simple solution allowed a highly stable measuringframework. As the tests were carried out at night, thetemperature was fairly constant and had no influence onsteel tube elongation. Additionally, in order to verify thevertical displacements measured on the tremie pipes, thedisplacements of the upper part of the GEWI steel profileswere measured geodetically. These are of course affected bythe steel elongation induced by the tensile load. After thesteel strains induced by the load are subtracted in themeasurements, both observations provided exactly the samedisplacement of the barrette.

The fibre-optic cables used were interrogated by Brillouinoptical time-domain analysis (BOTDA; for the relatedliterature, see Horiguchi et al. (1989), Niklès et al. (1997)and Niklès (2007)) and swept wavelength interferometry(SWI) measuring technology (for the related literature,see Froggatt & Moore (1998) and Gifford et al. (2007)).Both technologies adopt the principle that the temperature orstrain in a fibre-optic cable can be obtained from theinteraction between laser light and the glass fibre. TheBOTDA measuring technique requires the application oftwo light sources of different types – a pumping pulse(the pump) and continuous-wave light (the probe) – to thecable ends. The interrogator (Ditest from Omnisens)measures the backward Brillouin frequency shift generatedby the single pulse light when interacting with thecontinuous wave light, which varies depending on thechanging strain and temperature in the cable. The SWItechnology allows measurements only from one end of thecable. The interrogator (OBR4600 from Luna) uses SWI to

measure the Rayleigh backscatter as a function of lengthin the optical fibre. Changes in strain or temperaturecause time and spectral shifts in the local Rayleigh back-scattering. The OBR interrogator measures these shiftsand scales them to give a distributed temperature or strainmeasurement.The main macroscopic difference between these two

technologies is the resolution and sensor length: SWI(OBR4600 device) provides a resolution of 5 mm and amaximum sensor length of 70 m. With BOTDA (Ditestdevice), the resolution drops to 1 m, but the sensor can be upto 30 km long. The commercial cables used here weredeveloped by Iten (2011) in the framework of a dissertationat ETH Zurich, Switzerland. Technical details of implemen-tation of the SWI technology for geotechnical problems canbe found in Hauswirth (2015).

Test resultsThe TB was loaded step-wise up to a maximum load of

12 MN. The measured displacement for each loading step isplotted in Fig. 8(a). The waiting periods after each loadingstep were determined according to the requirements of thegeotechnical Swiss standard SN SIA 267-1 (SIA, 2013b). Inaccordance with the standard, the time-dependent displace-ment at constant load is plotted on a semi-logarithmicdiagram (Fig. 8(b)). The gradients of the plotted curvesrepresent the creep index (units: mm). If the displacementincrement between 5 and 15 min is less than 0·2 mm, theobservational period should be at least 15 min. Otherwise,the loading step should last until the displacement curveapproaches a straight line. If the inclination of that line (thecreep index) is lower than 1, the next loading step can beapplied. The failure load is determined when the creep indexis equal to 2 mm.The displacement between 5 and 15 min was higher

than 0·2 mm only in the last loading step (12 MN). After

(V) (H)

Tremie pipes

4·7 m

4·7 m

1·2 m

3·7 m

3·0 m

1·0 m

3·5 m

3·0 m

Excavationtrench

9·0 m

3·7 m

GEWI profiles foruplift

GEWI profiles

Barrette

Sheet piling profiles

Concrete basement

Fibre optic cable loopinside the barrette

(four vertical segments)

Guide walls

Tremie pipes(positioned on topof the TB)

Referencebeam

Steel frame

Load cell

(b)(a)

Fig. 6. (a) Dimensions of the excavation and the TB (V, vertical cross-section; H, horizontal cross-section). (b) Details of the loading apparatusand instrumentation

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(a) (d)

(b)

(c) (e)

Fig. 7. (a) Steel cages of the TBs and the eight GEWI bars used for the uplift. (b) Surface of the excavated rock after bentonite removal.(c) Casting of the barrette. (d) Loading frame and load cells. (e) Details of the LVDTs for measuring the uplift of the TB

6

5

4

3

2

1

0

Verti

cal d

ispl

acem

ent:

mm

Verti

cal d

ispl

acem

ent:

mm

0 5000Load: kN Time: min

(a) (b)

10 000 15 000 1 10 100

Uplift of TB1

Uplift of TB2

0·8

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0·4

0·3

0·2

0·1

0

12 010 kN

9808 kN

7638 kN

5415 kN

3204 kN

Creep rate = 1 mm

Fig. 8. (a) Load–displacement curve for the two tested barrettes, TB1 and TB2. (b) Time history of the displacement at constant load for TB1

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 7

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5 min, a steep increase in the displacement took place,whereas later the curve stabilised, approaching a straightline with inclination (creep index) almost equal to 1 mm. Thefibre-optical measurements showed that this increase wasmost probably due to the non-linear behaviour of theconcrete.

Both tests were terminated after 12 MN load withoutreaching failure (creep index= 2 mm), because, owing to thebearing limitations of the steel frame, no additional loadcould be applied.

An interesting insight into the problem of soil–structureinteraction is given by the fibre-optic measurements. Fig. 9(a)shows the development of the strains (measured with SWItechnology) in the TB during the last four loading stages. Thedashed straight lines represent the upper and lower sides ofthe wall. It can be clearly observed that between 5400 and7600 kN, the strains in the upper part of the barrette increasesignificantly.

In the same load range, the rate of displacement of theTB increases (Fig. 8(a)). Although the displacements arerelatively small, the peak strains measured with the SWImeasuring technique reach remarkable values of approxi-mately 2000 με. These measured strain values correspondvery well to the theoretical values that are obtainedif only the GEWI steel bars are stretched under theload (GEWI steel area AGEWI = 25 335 mm2, tension inthe steel at load N=12 MN, σt = 474 N/mm2, steel strainεGEWI= 2255 με).

The measured strain peaks with the SWI measuringtechniques correspond to the strain as if only the steel iswithstanding the load. Therefore, it can be concluded thatthe peaks in the strain correspond to cracks in the TB,as the concrete resistance makes no contribution to reducingthe strain in the GEWI bars. Generally, it can be clearly seenthat the area in which cracks are observed increases as theload becomes higher, and it reaches half of the vertical lengthof the TB at 12 MN load. Fig. 9(b) shows the deformation ofthe TB obtained by integrating the strains, which reached1·6 mm at 12 MN. Since the final uplift of the wall was4·6 mm, the total final heave of the bottom of the TB is about3·0 mm.

Comparison between the measurements obtained with theSWI and BOTDA technology (Figs 9(a), 10(a) and 10(b))shows that the latter is unable to detect the position of thecracks in the TB because the strains are measured over alength of 1 m, and not a few millimetres, as with SWI.Originally, only BOTDA measurements were planned,

because the non-linear behaviour of the concrete was notexpected and the Ditest device was considered more robustfor field application. However, as the measured strains inthe TB2 were much higher than would be predictedconsidering only the rock–concrete interaction and linearconcrete behaviour, it was also decided to use the SWIinterrogator OBR4600 to have a more in-depth look intothe structure (TB1). The failure load was expected to bearound 7–8 MN maximum, whereas in reality it was foundto be more than 12 MN (failure load was not reached in thetest). As explained in the next sections, the high bearingcapacity is due to dilatancy at the contact between rock andconcrete.In the following section, the test is modelled with the

FE code Abaqus, which allows a better understanding ofthe soil–structure interaction during loading. The resultsare validated against the closed-form solution for theload–displacement behaviour of a shaft pull-out test in rockaccording to the method of Kulhawy & Carter (1992). Theextrapolated failure load is determined by adopting ahyperbolic curve (Fleming, 1992).

MODELLINGFinite-element modelAn FEmodel of the rock and the TB was built with the FE

software Abaqus (Abaqus v6.14 (Abaqus, 2014)). Takingadvantage of the problem’s symmetry, only one-half ofthe TB and the rock was considered in the model(Figs 11(a) and 11(b)). The symmetry axis was positionedin the middle of the TB and cut its shortest side.The model depth is 20 m, the length is 9·6 m and the width

is 7·3 m. The dimensions were optimised to reduce the modelsize in order to prevent the boundaries affecting the results.The GEWI steel bars (four out of eight) and the vertical

8·5

9·0

9·5

10·0

10·0

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th: m

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(a) (b)

1500 2000 0 0·5 1·0 1·5 2·0 2·5

5415 kN

9808 kN

7638 kN

12 010 kN

5415 kN

9808 kN

7638 kN

12 010 kN

Fig. 9. (a) Vertical strains measured by the fibre-optical sensors (SWI interrogating technology) during the test at different loading stages.The plotted values are the average strains measured by four vertical segments. (b) Vertical deformation of TB1 obtained by integrating the strains.The dashed straight lines represent the upper and lower sides of the wall

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rebars of the steel cage were modelled as volume elementsinside the TB. The shape of the steel bars was chosen to bequadratic instead of their true circular shape in order toreduce the number of volume elements.Linear elements of type C3D4, a four-node linear tetra-

hedron, were adopted. Preliminary analysis had shownthat the use of quadratic elements produced less accurateprediction of the cracks inside the element. The mesh size of6·25 cm (for linear elements) corresponds to one-quarterof the horizontal rebar spacing. To study the influence ofthe mesh size, models with coarser mesh were also tested(12·5 and 25 cm). The effects of element size arediscussed later.

Constitutive modelsThe rock was modelled as a homogeneous medium with

a linear elastic constitutive model and non-associatedMohr–Coulomb failure criterion. This strong simplificationof the layered rock mass was necessary to obtain ahomogeneous and simple bearable value of the contactstrength for the design. No interface was modelled

between rock and concrete, and therefore full bonding wasassumed.The horizontal mesh element size at the contact between

the TB and the rock was chosen to be the same size as thedifference between the wider top and narrower bottomexcavated portions of the trench (10 cm). In this way, theshear distribution in the elements at the contact is optimisedand the elements represent a kind of volume elementinterface (see also Fig. 11(b)). The dilatancy, which in theanalysis is considered a homogeneous rock property, isin reality a property of the rough contact between rockand concrete. This simplification is justified by the goodreproduction through the FE analysis of the observedbehaviour of the TB during the tests. The dilatancy ofthe ‘glued’ rock elements at the contact with the TBreproduces well the increase in contact strength due to therough contact.For modelling the mechanical behaviour of the concrete,

the concrete damage plasticity model (CDP) was chosen(Tao & Chen, 2015). The parameter values for the compres-sive strength, stiffness and density of the adopted concrete(C30/37) were chosen according to default values and areshown in Table 2. The choice of default constant values ismotivated by the fact that compressive (shearing) failure isnot relevant for the current boundary value problem, sincefailure takes place only in tension. Only the tensile propertiesof the concrete are back-calculated in order to fit theexperimental results (see next section).The CDP model implemented in Abaqus allows yielding

in the concrete to be modelled: hardening in compressionbefore failure and stiffening in tension after failure. Themodel is formulated in the framework of plasticity theory,taking into account the effects of the cracks by means of adamage parameter, D, which reduces elastic stiffness afteryielding occurs. The Abaqus formulation allows the user’sown choice of hardening and softening (stiffening) rules to beimplemented.The adopted tensile strength and post-peak behaviour of

the concrete (obtained with inverse analysis of the exper-imental results) is described by equation (1). The pre-failurebehaviour (εt, εct) is modelled as linear elastic, while thepost-failure softening is predicted by the power load

7·3 m

20·0 m

9·6 m

1·2 m1·0 m

1·5 m 2·35 m

(a) (b)

Fig. 11. (a) Geometry of the adopted FE model (half-symmetrical).(b) Detail of the TB

8·5

9·0

9·5

10·0

10·0

10·5

11·5

12·0

12·5

13·0

Dep

th: m

8·5

9·0

9·5

10·0

10·0

10·5

11·5

12·0

12·5

13·0

Dep

th: m

0 1000ΔStrain: με

(a)

2000 0 1000ΔStrain: με

(b)

2000

5415 kN

9808 kN

7638 kN

12 010 kN

5415 kN

9808 kN

7638 kN

12 010 kN

Fig. 10. Vertical strains measured by the fibre-optical sensors (BOTDA interrogating technology) during the test in: (a) TB1 and (b) TB2 atdifferent loading stages. The dashed straight lines represent the upper and lower sides of the wall

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 9

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model proposed by Belarbi & Hsu (1994) and Belarbi et al.(1996).

σt ¼ fcrεctεt

� �m

ð1Þ

This equation is valid for εt� εct, where εct is the criticaltensile strain.

In equation (1), σt is the predicted stress, fcr and εcr are thetensile cracking stress and strain, m is the exponent whichregulates the drop rate of the strength against the strains andεt is the total strain.

The damage evolution (according to Lubliner et al. (1989))is calculated according to the following equation

D ¼ 1� σtfcr

ð2Þ

This equation is valid for σt� fcr.

Forward analysisThe FE analysis was carried out in two steps. In the first

calculation step, a gravity load is applied to the wholemodel, which takes into account the rock, the excavation andthe TB. This first step simulates: (a) the excavation underbentonite; (b) the casting of the TB under water; and (c)dredging of the bentonite. This simplified procedure wasadopted to allow a faster inverse analysis, after preliminaryanalysis proved that the three phases could be modelled in asingle step without significantly affecting the results of thenext pull-out step. In a second step, the pull-out wascarried out.

A simple forward analysis adopting the analyticalsolution proposed by Kulhawy & Carter (1992) was alsocarried out.

Inverse analysisThe inverse analysis was carried out by varying the

elastoplastic properties of the rock (elastic modulus, cohe-sion, friction and dilatancy angle) and the tensile strength( fcr and m) of the concrete. In the analytical solution, onlythe already mentioned rock elastoplastic properties werevaried. The initial values were those from the geologicalinvestigation described in Table 1.

The goal was to obtain the best possible match betweenmeasured vertical displacement (analytical and FE) andstrains of the TB (FE) for each applied loading step. Theanalysis was carried out manually rather than with anoptimisation algorithm.

The parameter variation was simplified by considering thefollowing important aspects.

Rock properties: the rock elastic properties mainly affectthe vertical strains in the TB before the cracks occur and theinclination of the load–displacement curve before yielding.The rock cohesion influences the yielding load, while frictionand in particular dilatancy regulates the gradient of the load–displacement curve after yielding (straight line for analyticalsolution).

Concrete properties: in the numerical analysis, the term fcrinfluences the crack initiation; therefore, it was varied to

obtain crack initiation in the model at the same load levelas in the experiment. The parameter m strongly influencesthe spatial development of the cracks, because it regulatesthe rate of strength drop after the failure occurs. Theexponent m was therefore varied to obtain a good agreementbetween calculated and measured cracked area for eachload level.

Inverse analysis resultsThe inverse analysis was first carried out by varying the

material parameter for obtaining the best fit betweenmeasured and calculated load–displacement (uplift) curve.The focus here was to determine the material properties ofthe rock.The best-fit load–displacement curves obtained with the

inverse analysis and FE as well as the analytical approach areshown in Figs 12(a) and 12(b), respectively. The analyticaland the numerical calculations were both carried out with thesame rock and (elastic) concrete properties.The back-calculated rock properties obtained with the

inverse analysis are shown in Table 3. Not surprisingly, theparameter values obtained with inverse analysis adoptingthe analytical and the numerical solutions are the same:the analytical Kulhawy and Carter approach represents theclosed-form solution of the adopted FE analysis when themechanical behaviour of the concrete is linear.It can be observed that the analytical solution predicts the

load–displacement behaviour of the TB during the test verywell, if the 1·6 mm final displacement due to the cracks in theconcrete is taken into account (Fig. 12(a)). As there is nocut-off deformation value for dilatancy, the FE model is notable to predict the failure. Failure is predicted instead with asimple hyperbolic curve (Fig. 12(b)).The failure load predicted with the formula proposed by

Fleming is 15 000 kN. The derivations are given in theAppendix.The model is capable of reproducing the acceleration in

the displacements, which takes place between 5400 and7600 kN.The second part of the inverse analysis was carried out by

varying the concrete tensile properties to obtain the best fitbetween measured and calculated strains (Figs 13(a)–13(c))as well as the deformation of the TB (Fig. 13(d)). Theback-calculated concrete tensile strength and softeningparameter m are equal to 2 N/mm2 and 0·9, respectively.Figure 13(a) shows the calculated and measured vertical

strains in the TB for the last two loading steps, before the firstcracks occur. The analysis was carried out with the optimisedparameters from the back-calculation of the load–displace-ment curve.The size and the area of extensions of the experimental and

calculated strains match quite well, although the predictedstrains at the bottom of the TB in the first loading steps arenegative. The strains in the FE calculation are negative(in Abaqus, compression is negative) because of the heave atthe bottom induced by the excavation. In the measurements,the strains at the bottom lie on the reference point and theyare set equal to zero.Figure 13(b) shows the strains measured in the four vertical

segments of the fibre-optical cable loop plotted against the

Table 2. Parameters adopted for modelling concrete according to the CDP model

Material γ: kN/m3 Ec: MN/m2 νc ϕ: degrees e f K

Concrete 24 33 000 0·15 35 0·1 1·16 0·667

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calculated strains. It can be observed that the spacing anddistribution of the measured strain where cracks occurhighly depend on the cable position. The comparisonbetween measured and calculated strains at two representa-tive loading stages during which cracks occurred is shownin Fig. 13(c). Fig. 13(d) illustrates the very good agreementbetween integrated and measured vertical displacement ofthe TB.The main advantage of the FE compared to the analytical

approach is therefore the ability to predict the non-linearbehaviour of reinforced concrete and the transition zonebetween initial and full slip at the contact.

Sensitivity analysis and discussionThe analysis allows the crucial contribution of the

contact dilatancy for the bearing capacity of the barretteto be identified. If the dilatancy is not taken into accountin the analysis, the failure takes place immediately afterthe contact reaches its maximum strength, long before themaximum applied load can be reached (see Fig. 12(a)). Thedevelopment of the calculated cracked area has been found tobe highly influenced by the post-failure behaviour of theconcrete. The failure of the TB under tension is preventedonly by the dilatancy, which allows strength increase duringyielding.

Table 3. Back-calculated rock properties

Material ρ: kN/m3 Er: MN/m2 νr ϕ′: degrees ψ: degrees c′: kN/m2

Rock 27 2000 0·2 32 10 280

0 1 2 3 4 5 6Vertical displacement: mm

20 00018 00016 00014 00012 00010 000

8000600040002000

0

Load

: kN

0 1 2 3 4 5 6Vertical displacement: mm

(a) (b)

20 00018 00016 00014 00012 00010 000

8000600040002000

0

Load

: kN

Results TB1

Results TB1

Kulhawy & Carter (1992),elastic behaviourKulhawy & Carter (1992),full slip behaviourKulhawy & Carter (1992),full slip + concrete cracksFleming (1992)

Estimated failure load(Fleming)

6·25 cm el. size

12·5 cm el. size

25 cm el. size

No dilatancy

Fig. 12. Back-calculation of displacements. (a) Finite-element simulation and measured displacement for TB1 for three different mesh sizes. Onecurve shows the results from a calculation carried out without taking into account dilatancy. (b) Analytical prediction of the displacementaccording to Kulhawy & Carter (1992) for the elastic and plastic slip. The prediction of the displacement and failure load according to Fleming(1992) is also plotted

–10 40

Strains: με Strains: με Strains: με Deformation: mm

(a) (b) (c) (d)

90 –100 400 900 1400 1900 2400 2900 –100 400 900 1400 1900 2400 2900 0 0·5 1·0 1·5 2·0 2·59·1

9·6

10·1

10·6

11·1

11·6

12·1

Dep

th: m

9·1

9·6

10·1

10·6

11·1

11·6

12·1

Dep

th: m

9·1

9·6

10·1

10·6

11·1

11·6

12·1

Dep

th: m

9·1

9·6

10·1

10·6

11·1

11·6

12·1

Dep

th: m

S1 3204 kN S1 12 010 kN S1 7638 kN

S1 12 010 kN

LE, mesh 6·5 cmL = 7638 kNLE, mesh 6·5 cmL = 12 010 kN

S1 7638 kN

S1 12 010 kN

LE, mesh 6·5 cmL = 7638 kNLE, mesh 6·5 cmL = 12 010 kN

S2 12 010 kN

S3 12 010 kN

S4 12 010 kN

LE, mesh 6·5 cmL = 12 010 kN

S1 5411 kN

LE, mesh 6·5 cmL = 3204 kNLE, mesh 6·5 cmL = 5415 kN

Fig. 13. Back-calculation of the strains: (a) measured and back-calculated vertical strains before the cracks occur; (b) measured (four measuredsegments, S1 to S4) and back-calculated strains for the final loading step of 12 MN. (c) Measured (S1) and back-calculated strains for 7·6 and12 MN loading stage. (d) Comparison of the integrated calculated and measured strains (displacement). L, load level; LE, linear element

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 11

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The simulated development of the yielding in the rockin the model is shown in Figs 14(a)–14(d). ComparingFigs 13(c) and 14(c), it can be observed that extensivecracking develops once all the rock elements at the contactreach yielding, which happens at approximately 7·6 MN load(60% of final load= 12 MN). This value also corresponds tothe failure load for the design pressure of 360 kPa and lateralsurface of 2� 3� 3 � 5 ¼ 21 m2.

The increase in the deviatoric strength can be clearlyobserved in Figs 14(e) and 14(f). Fig. 14(e) shows the stress–strain behaviour in a rock element (integration point) atthe contact with the rock. Owing to the effects of thedilatancy (increase in confining pressure), after yieldingoccurs (deviatoric stress q=600 kPa), the stress keepsincreasing as the deviatoric shearing strain gets higher.Fig. 14(f) shows the stress path followed in p′–q space,where q is the deviatoric stress and p′ is the mean (effective)total stress at the same integration point. The influence ofdilatancy after yield occurs can be clearly observed.

Thanks to the dilatancy, catastrophic failure of the contactis prevented, and the plastic strain areas in the rock continueto increase until the final loading step of 12 MN, at whichfailure still does not take place.

Figs 14(g) and 14(h) show the tensile damage inside the TBfor the two last loading states. These areas with reducedstiffness reproduce the effect of the cracks in the concrete andthe increase of deformation due to the reduced stiffness of thebarrette.

Quality controlAs it is well known that the results of a CDP model are

mesh-dependent (Tao & Chen, 2015), the influence of themesh size for the linear elements was studied, and the resultsare shown in Figs 12(a) and 15(a).The mesh size has almost no influence on the load–

displacement curve (Fig. 12(a)), but affects the prediction ofthe maximum strains inside the TB (Fig. 15(a)). This is notsurprising, as the influence of the crack is calculated inthe model as increased strains, and because the strainsare localised, these become higher the smaller the mesh sizebecomes. However, the fibre-optic sensors also allow thestrains to be measured over a length of 1 cm and do notdirectly measure across the crack width.The development of the cracked area and its extension is

not affected by the mesh size in the chosen range. Goodagreement between predicted and measured strains isobtained on reducing the mesh size to 6·25 cm. The fractureenergy is an important indicator for assessing the correctnessof crack prediction in concrete, in particular when constitu-tive models based on the damage concept are adopted. Thisshould lie in a realistic range.The calculated fracture energy in a portion of the damaged

area is shown in Fig. 15(b). The calculated energy in thiscracked TB is 206 N/m, which is in very good agreementwith the typical values for the adopted concrete calculatedaccording to the Féderation Internationale du Béton(fib, 2013).

1400

1200

1000

800

600

400

200

0

q: k

Pa

1400

1·0000·9170·8330·7500·6670·5830·5000·4170·3330·2500·1670·0830

1·0000·9170·8330·7500·6670·5830·5000·4170·3330·2500·1670·0830

1200

1000

800

600

400

200

0

q: k

Pa

0 0·01εs

0 200 400 600p'

0·02

(a) (b)

(c) (d)

(g)

(e) (f) (h)

Fig. 14. Yielding in the rock elements at loads of: (a) 3·2 MN; (b) 5·4 MN; (c) 7·6 MN; (d) 12 MN (quadratic element mesh). The differentsymbols show the different load levels for the point of contact where the stress–strain paths in (e) and (f) are calculated. The simulated cracks in theTB are shown in (g) and (h) for two representative loading stages

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SUMMARYAND CONCLUSIONSAn innovative retaining wall design was carried out for

stabilising a deep cut in a slope in the city centre of Zurich.The free-standing buttress wall was anchored to 14 barretteswith pre-stressed cables. The barrettes were positioned long-itudinally in the slope in the direction of their largest staticheight. FE analysis showed that the crucial contribution forthe stability of the structure was given by the contact strengthbetween the rock and the concrete of the barrettes. Therefore,two pull-out tests were carried out on two TBs of reduceddimensions built in front of the future foundation where thehighest contact shear stress was expected. Besides conven-tional instrumentation, distributed fibre-optic sensors werealso used. These allowed the non-linear behaviour of thereinforced concrete to be detected qualitatively and quanti-tatively during the test. These experimental results werecrucial for the interpretation and analysis of the test results.With the experimental results, an inverse analysis of rockproperties was carried out, based on an analytical and anumerical approach. An almost perfect match was achievedbetween the experimental results and the numerical as well asthe analytical calculation. As expected, it was found thatdilatancy at the rock–concrete interface allows much higher(almost double) strength to be reached than if only friction istaken into account. The higher strains that developed in theconcrete, during the phase in which contact dilatancy tookplace, induced cracks in the reinforced concrete.This contribution demonstrates that for correct interpret-

ation of experimental results from tensile pull-out tests, thenon-linear behaviour of the reinforced concrete can have aremarkable influence, and that distributed strain monitoringshould be implemented in the shaft.The contact strength adopted for the wall design was

confirmed by the tests and the analysis that were carried out.

ACKNOWLEDGEMENTSThe authors thank the ETH Zurich, in particular

Cristophe Hallier, for the opportunity to design and carry

out the tests. The excellent professional conduct and supportof the company Bauer, in particular Niklas Haag andAndreas Simson, were essential for building and carryingout the complex tests. The company Marmota EngineeringAG, in particular Frank Fischli, is gratefully acknowledgedfor instrumenting the TB and analysing the experimentaldata. Bernhard Trommer, Fred Baumeyer and Theo Kellerfrom Basler & Hofmann AG also made a substantialcontribution to the design of the wall. Melanie Prager isgratefully acknowledged for support in FE modelling of thereinforced concrete for the inverse analysis. The authors arealso grateful to Hansjörg Gysi for the careful review of theproject.

APPENDIXThe inverse analysis of the rock properties is validated adopting

the analytical approach described by Kulhawy & Carter (1992). Thismethod allows the displacement of a test shaft to be obtaineddirectly from the elastoplastic rock properties, the elastic concreteproperties and the applied load. The original contribution describesthe full meaning and derivation of the parameters, which is notrepeated in this Appendix.

The mechanical properties of the concrete and dimensions of thebarrette are as follows

l ¼ 3 m

b ¼ 1 m

t ¼ 3�5 m

Ec ¼ 33 000 MN=m2

νc ¼ 0�15

Ac ¼ lb ¼ 3 m2

9·1

9·6

10·1

10·6

LE, mesh 6·5 cmL = 12 010 kN

LE, mesh 12·5 cmL = 12 010 kN

11·1

11·6

12·1

Dep

th: m

–100 400 900 1400Strains: με

1900 2400 2900

2 500 000

2 000 000

1 500 000

1 000 000

500 000

00 0·00005 0·00010 0·00015

Crack length: m0·00020 0·00025 0·0030

Verti

cal t

ensi

le s

tress

: N/m

2

Fracture energy = 206 N/m

Energy

(a)

(b)

Fig. 15. (a) Prediction of vertical strains in the TB for the coarse and the fine mesh. (b) The fracture energy calculated in one damaged meshelement. The crack length is calculated from the measured strain multiplied by the mesh element size

IN SITU TESTING OF BARRETTE FOUNDATIONS FOR HIGH RETAINING WALL 13

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The adopted rock properties are described in Table 3.Because the formulas are only valid in a circular pile, the barrette

will be transformed into an equivalent circular pile

As ¼ 2l ¼ 6 m2=m

As is the area of the barrette wall skin surface; l is the length of thebarrette wall.

This leads to an equivalent diameter of a pile

dequ ¼ As

π¼ 1�91 m

This leads in turn to an equivalent cross-sectional area of the pile

Ac;equ ¼ d2equπ

4¼ 2�864 m2

which leads to an equivalent Young’s modulus

Ec;equ ¼ EcAc

Ac;equ¼ 34 557 MN=m2

Now the equations of Kulhawy & Carter (1992) can be applied.

μtð Þ2¼ 2ζ λ

� �2tdequ

� �2

ζ ¼ ln 5ð1� νrÞ tdequ

� �

λ ¼ Ec;equ=Gr

where Gr is shear modulus of the rock mass.The elastic uplift can be obtained by adopting the following

equation

Erdequwu

2Qu¼ 1

π� Er

Ec;equ� 2μdequ

� cosh ðμtÞsinh ðμtÞ

wu ¼ 1�443mm ðforQu ¼ 12000MNÞThis allows the theoretical displacement straight line for the

elastic uplift to be obtained (see also Fig. 12(b)).For the full slip behaviour, the following final displacement is

obtained

wu ¼ F5Qu

πErdequþ F6 dequ ¼ 2�952 mm ðforQu ¼ 12 000 MNÞ

F5 ¼ 4a3 � a1ðλ1dequC5 � λ2dequC6Þ ¼ 4�588

a1 ¼ 8�059

a2 ¼ 5�669

a3 ¼ 0�025

λ1 ¼ 0�086 1m

λ2 ¼ �0�092 1m

F6 ¼ a2cEr

¼ 0�00079

C5 ¼ �2�160

C6 ¼ �1�160

This allows the theoretical displacement straight line for the fullslip uplift to be obtained (see also Fig. 12(b)).

As shown in Fig. 12(b), the results from the analytical solution arevery close to the displacements obtained from the measurements(without the contribution of the cracks in the TB).

The failure load is predicted by matching the measured displace-ment with those predicted by the following greatly simplifiedhyperbolic equation (Fleming, 1992)

ΔS ¼ MSdequPS

US � PS

where ΔS is the pile head displacement; MS is a constant (accordingto Fleming, MS is 0·0005 for very stiff soils); DS is the equivalentdiameter = 1·91 m; PS is the current load level; and US is the failureload= 15 000 kN.

NOTATIONAc area of concrete barrette

Ac,equ area of equivalent circular pileAGEWI area of GEWI steel profiles

As skin surface of barrettec′ effective cohesionD damage

dequ diameter of equivalent circular pileE elastic Young’s modulus

EA1 soil active earth pressureEA2,H horizontal component of active rock pressureEA2,V vertical component of active rock pressure

Ec elastic Young’s modulus of concreteEc,equ elastic Young’s modulus of equivalent circular pileEP2,H horizontal component of passive rock pressureEP2,V vertical component of passive rock pressureEpl primary loading stiffnessEr elastic Young’s modulus of rock massEur unloading–reloading stiffnessE0 earth pressure at restf ratio of biaxial to uniaxial compressive strength

fcr critical tensile stress (uniaxial)Gr elastic shear modulus of rock massG1 weight of the wallG2 weight of the barrettes and the rock in betweenK second stress invariant ratioL load on the pile

MS tangent of the load at the origin of the hyperbolic functionm exponent of concrete softening power lawN tensile loadPS shaft loadp′ triaxial volumetric stress invariantQu uplift forceq triaxial deviatoric stress invariantqu uniaxial compressive strengthReq radius of the equivalent rotating mechanismR1 rock reaction on the steel concrete edgeR2 rock reaction at the bottom of the barrette foundationT resultant of the barrette skin frictiont depth of equivalent pile

US ultimate shaft frictionwu uplift deformation of base of test barretteγ dry density

ΔS settlement of shaft headεct critical strain (uniaxial)

εGEWI strain in the GEWI steel profilesεs deviatoric strainεt total tensile strain (uniaxial)ζ geometry factorλ pile/soil stiffness ratioν Poisson’s ratioνc Poisson’s ratio of concreteνr Poisson’s ratio of rock massρ dry densityσt tensile stress (uniaxial)ϕ friction angleψ dilatancy angle

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